ON STATISTICAL-ANALYSIS OF BOOLEAN MODELS WITH NONRANDOM GRAINS

A Boolean model with a non-random convex typical grain M is considered . Set-valued inside and outside estimators for the central symmetrizat ion M = {x - y: x, y is-an-element-of M} of M are proposed and their c onsistency in the Hausdorff metric is demonstrated. The estimation met hod is based on the evaluation of the empirical capacity functional an d an application of the Gilvenko-Cantelli theorem for random closed se ts. Generalizations for other models are given (Boolean models with a non-convex typical grain, multiphased Boolean models, non-stationary B oolean models etc.).